The PetDelights factory is known for its production of pet food. Its production line is designed to be highly efficient, allowing for a continuous flow of products from the mixing of ingredients to the final packaging of the product. However, recently, the machine responsible for the packaging stage has begun to experience intermittent technical failures, which have significantly impacted the efficiency of the production process. Due to these failures, an increase in the time required to package products has been observed. In fact, this packaging time has increased to an average of 40 seconds per product, which is affecting the factory's production capacity, generating delays and potential financial losses. To assess the impact of these failures on production, the company has decided to model the packaging time of each product as a random variable T, which follows an Exponential distribution with a mean μ = 40 seconds. a. Explicitly write the probability density function of the random variable T, using seconds as the time unit. b. Calculate the probability that the packaging time for a product will be greater than one minute. c. Calculate the probability that the packaging time for a product will be between 45 and 55 seconds.
The PetDelights factory is known for its production of pet food. Its production line is designed to be highly efficient, allowing for a continuous flow of products from the mixing of ingredients to the final packaging of the product. However, recently, the machine responsible for the packaging stage has begun to experience intermittent technical failures, which have significantly impacted the efficiency of the production process. Due to these failures, an increase in the time required to package products has been observed. In fact, this packaging time has increased to an average of 40 seconds per product, which is affecting the factory's production capacity, generating delays and potential financial losses. To assess the impact of these failures on production, the company has decided to model the packaging time of each product as a random variable T, which follows an Exponential distribution with a mean μ = 40 seconds. a. Explicitly write the probability density function of the random variable T, using seconds as the time unit. b. Calculate the probability that the packaging time for a product will be greater than one minute. c. Calculate the probability that the packaging time for a product will be between 45 and 55 seconds.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
Related questions
Question
Transcribed Image Text:The PetDelights factory is known for its production of pet food. Its production line is designed to be
highly efficient, allowing for a continuous flow of products from the mixing of ingredients to the final
packaging of the product. However, recently, the machine responsible for the packaging stage has
begun to experience intermittent technical failures, which have significantly impacted the efficiency
of the production process. Due to these failures, an increase in the time required to package
products has been observed. In fact, this packaging time has increased to an average of 40 seconds
per product, which is affecting the factory's production capacity, generating delays and potential
financial losses. To assess the impact of these failures on production, the company has decided to
model the packaging time of each product as a random variable T, which follows an Exponential
distribution with a mean μ = 40 seconds.
a. Explicitly write the probability density function of the random variable T, using seconds as the time
unit.
b. Calculate the probability that the packaging time for a product will be greater than one minute.
c. Calculate the probability that the packaging time for a product will be between 45 and 55 seconds.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps
Recommended textbooks for you
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON